On the limit distributions of continuous-state branching processes with immigration

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Keller-Ressel, Martin¹  Mijatovic, Aleksandar² 

[1] TU Berlin, Dept Math, Berlin, Germany

[2] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

关键词: Branching processes with immigration;    Limit distribution;    Stationary distribution;    Self-decomposable distribution;    Spectrally positive Levy process;    Scale function;    Infinitesimal generator;   

DOI  :  10.1016/j.spa.2012.03.012

来源: Elsevier

【 摘 要 】

We consider the class of continuous-state branching processes with immigration (CBI-processes), introduced by Kawazu and Watanabe (1971) [10] and their limit distributions as time tends to infinity. We determine the Levy-Khintchine triplet of the limit distribution and give an explicit description in terms of the characteristic triplet of the Levy subordinator and the scale function of the spectrally positive Levy process, which describe the immigration resp. branching mechanism of the CBI-process. This representation allows us to describe the support of the limit distribution and characterize its absolute continuity and asymptotic behavior at the boundary of the support, generalizing several known results on self-decomposable distributions. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free